Team:ETH Zurich/modeling/xor

From 2014.igem.org

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== Transfer Function ==
== Transfer Function ==
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=== Determistic Differential Equations ===
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We modeled the XOR gate module deterministically. Thus, we considered a continuous approximation of variables, like the number of integrases-DNA binding sites or the number of terminator. We wrote them as concentration. The transfer function obtained  
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We modeled the XOR gate module deterministically. Thus, we considered a continuous approximation of variables, like the number of integrases-DNA binding sites or the number of terminator. We wrote them as concentration. We do not take the species LasI and mRNA<sub>LasI</sub> into account because they are only produced by the XOR biologic gate and GFP is another product of this biologic gate that can be read out.
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$$\begin{align*}
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\frac{d[T_{on,i}]}{dt}&= -k_{ToffBxb1}[T_{on,i}][SA_{Bxb1}]^2 -k_{Toff\phi C31} [T_{on,i}][SA_{\phi C31}]^2 \\
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\frac{d[T_{offBxb1}]}{dt}&=k_{ToffBxb1} [T_{on,i}][SA_{Bxb1}]^2 -  k_{-ToffBxb1} [T_{offBxb1}] [SA_{\phi C31}]^2\\
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\frac{d[T_{off\phi C31}]}{dt}&=k_{Toff\phi C31} [T_{on,i}][SA_{\phi C31}]^2 -  k_{-Toff\phi C31} [T_{offBxb1}] [SA_{Bxb1}]^2\\
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\frac{d[T_{on,f}]}{dt}&=  k_{-ToffBxb1} [T_{offBxb1}] [SA_{\phi C31}]^2 + k_{-Toff\phi C31} [T_{offBxb1}] [SA_{Bxb1}]^2\\
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\frac{d[mRNA_{GFP}]}{dt}&=  k_{mRNA_{GFP}} (\frac{[T_{offBxb1}]}{\theta + [T_{offBxb1}]} +  \frac{[T_{off\phi C31}]}{\theta + [T_{off\phi C31}]}) - d_{mRNA_{GFP}}[mRNA_{GFP}]\\
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\frac{d[GFP]}{dt}&=  k_{GFP} [mRNA_{GFP}] - d_{GFP}[GFP]\\
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\end{align*}$$
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<br/>
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As there is a strong codon bias in both integrases' seuquences <sup>[[Team:ETH_Zurich/project/references|[14]]]</sup>, the flipping parameters were assumed such that they would not be a rate limiting step. (see the [https://2014.igem.org/Team:ETH_Zurich/modeling/parameters parameter pages for a summary of our parameters)
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=== Deterministic simulation ===
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At steady state, the transfer function obtained by simulation is shown on the next figure. It is remarkable to see that even a little amount of one integrase is sufficient to switch the XOR gate on.
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<br>
[[File:ETHZ_XORmodule.png|center|600px|thumb|The behaviour of XOR module as a function of activated Bxb1 sites (SABxb1) and ΦC31 sites (SAΦC31). The XOR behaviour is continuous since we modelled it deterministically.]]
[[File:ETHZ_XORmodule.png|center|600px|thumb|The behaviour of XOR module as a function of activated Bxb1 sites (SABxb1) and ΦC31 sites (SAΦC31). The XOR behaviour is continuous since we modelled it deterministically.]]

Revision as of 11:47, 14 October 2014

iGEM ETH Zurich 2014